
It is a well-known result that the spectral radius of \({{M}}\)  is the greatest lower bound for all
of its matrix norms, e.g. see Theorem 6.5.9 in [1]}. Letting \(\left| \left|\cdot \right| \right|\)  be
a matrix norm on \(N\times N\)  matrices, we have that
\({\rho }({{M}}) \le \left| \left|{{M}}\right| \right|.\) 
